Chapter Review
Chapter
Chapter 1
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Chapter Review
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Solutions 50 Videos

Determine whether each relation is a function, and state its domain and range.

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Q1a

Determine whether each relation is a function, and state its domain and range.

\displaystyle 3x^2 + 2y =6

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Q1b

Determine whether each relation is a function, and state its domain and range.

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Q1c

Determine whether each relation is a function, and state its domain and range.

\displaystyle x = 2^y

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Q1d

A cell phone company charges a monthly fee of $30, plus $0.02 per minute of call time.

a) Write the monthly cost function, C(t), where t is the amount of time in minutes of call time during a month.

b) Find the domain and range of C.

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Q2

Graph f(x) = 2|x + 3| -1, and state the domain and range.

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Q3

Describe this interval using absolute value notation.

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Q4

For the pair of functions, give a characteristic that the two functions have in common and a characteristic that distinguishes them.

\displaystyle f(x) =x^2 and \displaystyle g(x) = \sin x

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Q5a

For the pair of functions, give a characteristic that the two functions have in common and a characteristic that distinguishes them.

\displaystyle f(x) =\frac{1}{x} and \displaystyle g(x) = x

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Q5b

For the pair of functions, give a characteristic that the two functions have in common and a characteristic that distinguishes them.

\displaystyle f(x) =x^2 and \displaystyle g(x) = \sin x

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Q5c

For the pair of functions, give a characteristic that the two functions have in common and a characteristic that distinguishes them.

\displaystyle f(x) =2^x and \displaystyle g(x) = x

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Q5d

Identify the intervals of increase/decrease, the symmetry, and the domain and rage of each function.

\displaystyle f(x) = 3x

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Q6a

Identify the intervals of increase/decrease, the symmetry, and the domain and range of each function.

\displaystyle f(x) = x^2+ 2

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Q6b

For each of the following equations, state the parent function and the transformations that were applied. Graph the transformed function.

\displaystyle f(x) =|x + 1|

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Q7a

For each of the following equations, state the parent function and the transformations that were applied. Graph the transformed function.

\displaystyle f(x) = -0.25\sqrt{3(x+ 7)}

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Q7b

For each of the following equations, state the parent function and the transformations that were applied. Graph the transformed function.

\displaystyle f(x) = -2\sin(3x) + 1, 0 \leq x \leq 360^o

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Q7c

For each of the following equations, state the parent function and the transformations that were applied. Graph the transformed function.

\displaystyle f(x) = 2^{-2x} -3

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Q7d

The graph of y = x^2 is horizontally stretched by a factor of 2, reflected in the x—axis, and shifted 3 units down. Find the equation that results from the transformation, and graph it.

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Q8

(2, 1) is a point on the graph of y =f(x). Find the corresponding point on the graph of each of the following functions.

\displaystyle y = -f(-x)+2

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Q9a

(2, 1) is a point on the graph of y =f(x). Find the corresponding point on the graph of each of the following functions.

\displaystyle y =f(-2(x+ 9)) - 7

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Q9b

(2, 1) is a point on the graph of y =f(x). Find the corresponding point on the graph of each of the following functions.

\displaystyle y =f(x -2) + 2

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Q9c

(2, 1) is a point on the graph of y =f(x). Find the corresponding point on the graph of each of the following functions.

\displaystyle y = 0.3f(5(x-3))

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Q9d

(2, 1) is a point on the graph of y =f(x). Find the corresponding point on the graph of each of the following functions.

\displaystyle y = 1 -f(1-x)

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Q9e

(2, 1) is a point on the graph of y =f(x). Find the corresponding point on the graph of each of the following functions.

\displaystyle y = -f(2(x - 8))

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Q9f

For the point on a function, state the corresponding point on the inverse relation.

(1, 2)

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Q10a

For the point on a function, state the corresponding point on the inverse relation.

(-1, -9)

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Q10b

For the point on a function, state the corresponding point on the inverse relation.

(0, 7)

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Q10c

For the point on a function, state the corresponding point on the inverse relation.

f(5) = 7

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Q10d

For the point on a function, state the corresponding point on the inverse relation.

g(0) = -3

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Q10e

For the point on a function, state the corresponding point on the inverse relation.

h(1) = 10

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Q10f

Given the domain and range of a function, state the domain and range of the inverse relation.

D = \{x\in \mathbb{R}\}, \displaystyle R = \{y \in \mathbb{R}, -2 < y < 2\}

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Q11a

Given the domain and range of a function, state the domain and range of the inverse relation.

D = \{x\in \mathbb{R}, x \geq 7\}, \displaystyle R = \{y \in \mathbb{R}, y < 12\}

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Q11b

Graph the function and its inverse relation on the same set of axes. Determine whether the inverse relation is a function.

f(x) = x^2 -4

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Q12a

Graph the function and its inverse relation on the same set of axes. Determine whether the inverse relation is a function.

f(x) = 2^x

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Q12b

Find the inverse of each function.

f(x) = 2x + 1

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Q13a

Find the inverse of each function.

f(x) = x^3

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Q13b

Graph the following function. Determine whether it is discontinuous and, if so, where. State the domain and the range of the function.

\displaystyle f(x) = \begin{cases} &2x, &\text{when } x < 1 \\ &x +1, &\text{when } x \geq 1 \end{cases}

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Q14

Write the algebraic representation for the following piecewise function, using function notation.

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Q15

If

\displaystyle f(x) = \begin{cases} &x^2 +1, &\text{when } x < 1 \\ &3x, &\text{when } x \geq 1 \end{cases}

is f(x) continuous at x =1? Explain.

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Q16

A telephone company charges $30 a month and gives the customer 200 free call minutes. After the 200 min, the company charges $0.03 a minute.

a) Write the function using function notation.

b) Find the cost for talking 350 min in a month.

c) Find the cost for talking 180 min in a month.

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Q17

Given f = \{(0, 6), (1, 3), (4, 7), (5, 8)\} and g= \{(-1, 2), (1, 5), (2, 3) ,(4, 8), (8, 9)\}, determine

f(x) + g(x)

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Q18a

Given f = \{(0, 6), (1, 3), (4, 7), (5, 8)\} and g= \{(-1, 2), (1, 5), (2, 3) ,(4, 8), (8, 9)\}, determine

f(x)- g(x)

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Q18b

Given f = \{(0, 6), (1, 3), (4, 7), (5, 8)\} and g= \{(-1, 2), (1, 5), (2, 3) ,(4, 8), (8, 9)\}, determine

f(x)\cdot g(x)

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Q18c

Given f(x) = 2x^2 -2x, -2 \leq x \leq 3 and g(x) = -4x, -3 \leq x \leq 5, graph the following.

f

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Q19a

Given f(x) = 2x^2 -2x, -2 \leq x \leq 3 and g(x) = -4x, -3 \leq x \leq 5, graph the following.

g

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Q19b

Given f(x) = 2x^2 -2x, -2 \leq x \leq 3 and g(x) = -4x, -3 \leq x \leq 5, graph the following.

f +g

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Q19c

Given f(x) = 2x^2 -2x, -2 \leq x \leq 3 and g(x) = -4x, -3 \leq x \leq 5, graph the following.

f -g

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Q19d

Given f(x) = 2x^2 -2x, -2 \leq x \leq 3 and g(x) = -4x, -3 \leq x \leq 5, graph the following.

fg

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Q19e

f(x) = x^2 +2x and g(x) = x + 1. Match the answer with the operation.

\displaystyle \begin{array}{llllllll} &(a) \phantom{.} x^3 + 3x^2 + 2x &A \phantom{.} f(x) + g(x) \\ &(b) \phantom{.} -x^2 -x + 1 &A \phantom{.} f(x) - g(x) \\ &(c) \phantom{.} x^2 +3x + 1 &A \phantom{.} g(x) - f(x) \\ &(d) \phantom{.} x^2 +x - 1 &A \phantom{.} g(x) \times f(x) \end{array}

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Q20

f(x) = x^3 +2x^2 and g(x) = -x + 6.

a) Complete the table.

b) Use the table to graph f(x) and g(x) on the same axes.

c) Graph (f 1 g)(x) on the same axes as part b).

d) State the equation of (f + g)(x).

e) Verify the equation of (f + g)(x) using two of the ordered pairs in the table.

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Q21